# Properties

 Label 912.2.k Level $912$ Weight $2$ Character orbit 912.k Rep. character $\chi_{912}(607,\cdot)$ Character field $\Q$ Dimension $20$ Newform subspaces $8$ Sturm bound $320$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$912 = 2^{4} \cdot 3 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 912.k (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$76$$ Character field: $$\Q$$ Newform subspaces: $$8$$ Sturm bound: $$320$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$, $$31$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(912, [\chi])$$.

Total New Old
Modular forms 172 20 152
Cusp forms 148 20 128
Eisenstein series 24 0 24

## Trace form

 $$20 q + 20 q^{9} + O(q^{10})$$ $$20 q + 20 q^{9} + 20 q^{25} + 20 q^{49} + 4 q^{57} + 56 q^{61} + 8 q^{73} - 24 q^{77} + 20 q^{81} - 24 q^{85} + 56 q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(912, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
912.2.k.a $2$ $7.282$ $$\Q(\sqrt{-2})$$ None $$0$$ $$-2$$ $$-4$$ $$0$$ $$q-q^{3}-2q^{5}+2\beta q^{7}+q^{9}-\beta q^{11}+\cdots$$
912.2.k.b $2$ $7.282$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$0$$ $$0$$ $$q-q^{3}+2\zeta_{6}q^{7}+q^{9}+2\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots$$
912.2.k.c $2$ $7.282$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$6$$ $$0$$ $$q-q^{3}+3q^{5}+\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots$$
912.2.k.d $2$ $7.282$ $$\Q(\sqrt{-2})$$ None $$0$$ $$2$$ $$-4$$ $$0$$ $$q+q^{3}-2q^{5}-2\beta q^{7}+q^{9}+\beta q^{11}+\cdots$$
912.2.k.e $2$ $7.282$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$0$$ $$0$$ $$q+q^{3}-2\zeta_{6}q^{7}+q^{9}-2\zeta_{6}q^{11}-2\zeta_{6}q^{13}+\cdots$$
912.2.k.f $2$ $7.282$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$6$$ $$0$$ $$q+q^{3}+3q^{5}-\zeta_{6}q^{7}+q^{9}+3\zeta_{6}q^{11}+\cdots$$
912.2.k.g $4$ $7.282$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$-4$$ $$-2$$ $$0$$ $$q-q^{3}-\beta _{3}q^{5}+\beta _{1}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots$$
912.2.k.h $4$ $7.282$ $$\Q(\sqrt{-3}, \sqrt{-11})$$ None $$0$$ $$4$$ $$-2$$ $$0$$ $$q+q^{3}-\beta _{3}q^{5}+\beta _{1}q^{7}+q^{9}+\beta _{1}q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(912, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(912, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(76, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(228, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(304, [\chi])$$$$^{\oplus 2}$$